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Design an arrangement of display boards in the school hall which fits the requirements of different people.

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A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

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Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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Every day at noon a boat leaves Le Havre for New York while another boat leaves New York for Le Havre. The ocean crossing takes seven days. How many boats will each boat cross during their journey?

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Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

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Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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A bus route has a total duration of 40 minutes. Every 10 minutes, two buses set out, one from each end. How many buses will one bus meet on its way from one end to the other end?

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I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?

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Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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How will you go about finding all the jigsaw pieces that have one peg and one hole?

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An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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What is the best way to shunt these carriages so that each train can continue its journey?

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This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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Can you fit the tangram pieces into the outline of this teacup?

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How many different triangles can you make on a circular pegboard that has nine pegs?

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Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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Can you fit the tangram pieces into the outline of Mah Ling?

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Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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What is the greatest number of squares you can make by overlapping three squares?

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Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?

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In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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Can you fit the tangram pieces into the outlines of the people?

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Can you make a 3x3 cube with these shapes made from small cubes?

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Can you fit the tangram pieces into the outline of the house?

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Can you find a way of counting the spheres in these arrangements?

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Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

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An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

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A shape and space game for 2, 3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board.

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Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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Which of these dice are right-handed and which are left-handed?

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A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

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Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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How many different symmetrical shapes can you make by shading triangles or squares?

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These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

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Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

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Can you fit the tangram pieces into the outlines of the convex shapes?

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Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

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We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

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How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?